A lithographic apparatus is a machine that applies a desired pattern onto a target portion of a substrate. Lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In that circumstance, a patterning device, such as a mask, may be used to generate a circuit pattern corresponding to an individual layer of the IC, and this pattern can be imaged onto a target portion (e.g. comprising part of, one or several dies or fields) on a substrate (e.g. a silicon wafer) that has a layer of radiation-sensitive material (resist). In general, a single substrate will contain a network of adjacent target portions that are successively exposed. Known lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion in at one time, and so-called scanners, in which each target portion is irradiated by scanning the pattern through the projection beam in a given direction (the “scanning”-direction) while synchronously scanning the substrate parallel or anti-parallel to this direction.
Many industrial processes, such as lithography, involve motion of a movable part along a trajectory that is defined by precise positions at specific times, e.g., set-points. Typically, the motion is performed by a closed loop controlled servo system comprising a motor with an amplifier, mechanics to be actuated (e.g., a slider), a position (and or velocity) sensor, a feedback and feed-forward controller and a set point generator. The motor receives the input from the controller that calculates the motor input as a function of the difference between the set point position and the measured actual position. Feedback control ensures that the actual position will become equal to the desired commanded set point position. Feedback control also can ensure the system's performance to be less sensitive to process uncertainties and disturbances.
A method for determining set-point data for such a movable part can be referred to as ‘trajectory planning’ and the resulting set-point data can be referred to as the ‘trajectory’. Typically motion signals to be applied to one or more actuators, e.g., one or more linear or planar motors, of the movable part are determined from the set-point data of the trajectory although not necessary in all circumstances. The motion signals, e.g. set-point signals, are then applied to the actuator to move the movable part to the desired positions.
An important aspect of trajectory planning is the ‘settling behavior’, i.e., the settling period. After a trajectory has reached an end or intermediate position, it takes a certain amount of time before the actual position is close enough to the required position. So, for example, after changing position, the system needs some “settling time” to reach the required positional accuracy. A similar observation can be made for a substantially constant velocity phase of a motion. During an acceleration (whether positive or negative), it takes a certain time for the velocity to settle to a substantially constant value. So, when considering high accuracy motion control, it is usually necessary to specify a ‘settling period’, the duration of which is determined by the settling behavior, which is a function of, among other possible things, the control loop, the applied acceleration and jerk, process uncertainties and disturbances, and by the required accuracy of positioning. Improvement of the settling behavior will result in a shorter duration of the settling period.
As an example, motion trajectories are often applied to the substrate and mask in a step-and-scan lithography apparatus. In a typical such apparatus, the substrate surface is exposed in a sequence of field scans. The exposure of each field requires that the substrate and mask be simultaneously scanned at precisely synchronized, substantially constant velocities. After each field exposure, the substrate stage is stepped from an initial state (i.e., a position and velocity) at the end of a field scan, to a new state (i.e., a new position and typically same velocity) at the start of the next field scan. Similarly, the mask stage is also stepped from an initial state at the end of a field scan, to a new state at the start of the next field scan.
To maximize processing of substrates per unit time in a lithographic apparatus, i.e., substrate throughput, it is desirable to expose a substrate in the minimum possible time. However, a lithographic apparatus also requires high precision positioning of the substrate and the mask. Accordingly, the object tables supporting the mask and/or the substrate should be moved smoothly, particularly during critical phases such as exposure, to produce a minimum amount of vibration in the lithographic apparatus. The unavoidable acceleration (whether positive or negative) of the object tables can produce vibrations in the lithographic apparatus that take a significant “settling time” before the position or velocity error is within the required accuracy.
FIGS. 2a to 2d show respectively example position, velocity, acceleration, and jerk trajectory profiles of an object table during an example conventional scan. The Y axis of each of FIGS. 2a to 2d represent the position, velocity, acceleration, and jerk respectively of the object table with respect to time, which is represented along the X axis of each of the Figures.
As shown in FIG. 2a, the object table moves from position 0 to +D between times t0 and t9. As shown in FIG. 2b, the object table moves at a substantially constant velocity +V between times t4 and t6 (the time period for exposure) and is stationary before time t1 and after time t9. As shown in FIG. 2c, the positive acceleration of the object table increases in a linear manner from time t1 until a maximum substantially constant positive acceleration +A is reached at time t2, from times t2 to t3 the object table positively accelerates at maximum positive acceleration +A, and then at time t3 the positive acceleration of the object table reduces until it is back at 0 at time t4. At time t4, the object table has a substantially constant velocity +V (shown in FIG. 2b). At time t6, the negative acceleration of the object table linearly increases from time t6 until a maximum negative acceleration −A is reached at time t7, from times t7 to t8 the object table negatively accelerates at maximum negative acceleration −A, and then at time t8 the negative acceleration of the object table decreases until it is back at 0 at time t9.
As shown in FIG. 2d, the jerk on the object table is at maximum positive jerk +J from times t1 to t2, at maximum negative jerk −J from times t3 to t4, and 0 between times t2 to t3 and times t4 to t6. Similarly, the jerk on the object table is at a maximum negative jerk −J from times t6 to t7, at a maximum positive jerk +J from times t8 to t9, and 0 between times t7 and t8. Thus, there are discontinuities in the jerk at times t1, t2, t3 and t4 (as well as at t6, t7, t8, and t9) which cause discontinuities in the motion of the object table. Such discontinuities and large jerk values can cause vibrations in the lithographic apparatus, vibrations that can have an effect on the accurate positioning of the object table.
Consequently, a settling period is provided between times t4 and t5 (just before exposure) during which vibrations, such as generated during the acceleration (whether positive or negative) of the object table, are allowed to dissipate and the velocity can settle to substantially +V. The amount of settling period the object table requires to reach a substantially constant scanning velocity depends to a large part on the settling behavior that is the result from, among other possible things, the applied acceleration and jerk, an possible feed-forward, the mechanical system properties and the bandwith of the control system. However, the larger the settling period, the larger the time for the object table to complete a repetitive motion and the smaller the throughput of the lithographic apparatus.